Systems of Inequalities Practice

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

Front

What does the graph of x < -1 look like?

Back

The graph of x < -1 is a vertical line at x = -1, with shading to the left, indicating all values less than -1.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

To determine if a point is a solution, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What does it mean if a system of equations has no solution?

Back

If a system of equations has no solution, it means the lines are parallel and will never intersect.

Front

What is the solution to the system of inequalities: x + 2y ≥ 4 and 3x − 2y < 4?

Back

The solution includes all points that satisfy both inequalities, which can be found by graphing.

Front

What is the significance of the boundary line in a graph of an inequality?

Back

The boundary line represents the values where the inequality changes from true to false. It is solid for '≥' or '≤' and dashed for '>' or '<'.

Front

How do you graph the inequality y < 2x + 3?

Back

Graph the line y = 2x + 3 as a dashed line, then shade below the line to represent all points where y is less than 2x + 3.

Front

What is the difference between '≥' and '>' in inequalities?

Back

'≥' means 'greater than or equal to', including the boundary, while '>' means 'greater than', excluding the boundary.

Front

How can you find the intersection of two lines represented by equations?

Back

To find the intersection, solve the equations simultaneously to find the point (x, y) where they meet.

Front

What does the graph of y = 3x + 1 look like?

Back

It is a straight line with a slope of 3 and a y-intercept of 1, rising steeply as x increases.